Here is a pair of differential equations that Version 3 could not solve
(actually, it was still trying after 15 minutes on a 400 MHz PII!)
w:=Exp[-a x];
DSolve[{u'[x]==-u[x]+v[x]+w (1-a)+Cos[Pi x]-(1+Pi) Sin[Pi x],
v''''[x]==u[x]+v[x]+(Pi^4-1) Sin[Pi x]-Cos[Pi x]-w, u[0]==2,
v[0]==0,v''[0]==0,v[1]==0,v''[1]==0},
{u[x],v[x]},x]
These are linear equations with constant coefficients, and the exact solution
is
u=w+cos(Pi x), v=sin(Pi x)
I would appreciate someone running this calculation in Version 4.
N. Shamsundar
University of Houston